// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_GENERIC_PACKET_MATH_H
#define EIGEN_GENERIC_PACKET_MATH_H

namespace Eigen {

namespace internal {

/** \internal
 * \file GenericPacketMath.h
 *
 * Default implementation for types not supported by the vectorization.
 * In practice these functions are provided to make easier the writing
 * of generic vectorized code.
 */

#ifndef EIGEN_DEBUG_ALIGNED_LOAD
#define EIGEN_DEBUG_ALIGNED_LOAD
#endif

#ifndef EIGEN_DEBUG_UNALIGNED_LOAD
#define EIGEN_DEBUG_UNALIGNED_LOAD
#endif

#ifndef EIGEN_DEBUG_ALIGNED_STORE
#define EIGEN_DEBUG_ALIGNED_STORE
#endif

#ifndef EIGEN_DEBUG_UNALIGNED_STORE
#define EIGEN_DEBUG_UNALIGNED_STORE
#endif

struct default_packet_traits
{
	enum
	{
		HasHalfPacket = 0,

		HasAdd = 1,
		HasSub = 1,
		HasShift = 1,
		HasMul = 1,
		HasNegate = 1,
		HasAbs = 1,
		HasArg = 0,
		HasAbs2 = 1,
		HasAbsDiff = 0,
		HasMin = 1,
		HasMax = 1,
		HasConj = 1,
		HasSetLinear = 1,
		HasBlend = 0,
		// This flag is used to indicate whether packet comparison is supported.
		// pcmp_eq, pcmp_lt and pcmp_le should be defined for it to be true.
		HasCmp = 0,

		HasDiv = 0,
		HasSqrt = 0,
		HasRsqrt = 0,
		HasExp = 0,
		HasExpm1 = 0,
		HasLog = 0,
		HasLog1p = 0,
		HasLog10 = 0,
		HasPow = 0,

		HasSin = 0,
		HasCos = 0,
		HasTan = 0,
		HasASin = 0,
		HasACos = 0,
		HasATan = 0,
		HasSinh = 0,
		HasCosh = 0,
		HasTanh = 0,
		HasLGamma = 0,
		HasDiGamma = 0,
		HasZeta = 0,
		HasPolygamma = 0,
		HasErf = 0,
		HasErfc = 0,
		HasNdtri = 0,
		HasBessel = 0,
		HasIGamma = 0,
		HasIGammaDerA = 0,
		HasGammaSampleDerAlpha = 0,
		HasIGammac = 0,
		HasBetaInc = 0,

		HasRound = 0,
		HasRint = 0,
		HasFloor = 0,
		HasCeil = 0,
		HasSign = 0
	};
};

template<typename T>
struct packet_traits : default_packet_traits
{
	typedef T type;
	typedef T half;
	enum
	{
		Vectorizable = 0,
		size = 1,
		AlignedOnScalar = 0,
		HasHalfPacket = 0
	};
	enum
	{
		HasAdd = 0,
		HasSub = 0,
		HasMul = 0,
		HasNegate = 0,
		HasAbs = 0,
		HasAbs2 = 0,
		HasMin = 0,
		HasMax = 0,
		HasConj = 0,
		HasSetLinear = 0
	};
};

template<typename T>
struct packet_traits<const T> : packet_traits<T>
{};

template<typename T>
struct unpacket_traits
{
	typedef T type;
	typedef T half;
	enum
	{
		size = 1,
		alignment = 1,
		vectorizable = false,
		masked_load_available = false,
		masked_store_available = false
	};
};

template<typename T>
struct unpacket_traits<const T> : unpacket_traits<T>
{};

template<typename Src, typename Tgt>
struct type_casting_traits
{
	enum
	{
		VectorizedCast = 0,
		SrcCoeffRatio = 1,
		TgtCoeffRatio = 1
	};
};

/** \internal Wrapper to ensure that multiple packet types can map to the same
	same underlying vector type. */
template<typename T, int unique_id = 0>
struct eigen_packet_wrapper
{
	EIGEN_ALWAYS_INLINE operator T&() { return m_val; }
	EIGEN_ALWAYS_INLINE operator const T&() const { return m_val; }
	EIGEN_ALWAYS_INLINE eigen_packet_wrapper() {}
	EIGEN_ALWAYS_INLINE eigen_packet_wrapper(const T& v)
		: m_val(v)
	{
	}
	EIGEN_ALWAYS_INLINE eigen_packet_wrapper& operator=(const T& v)
	{
		m_val = v;
		return *this;
	}

	T m_val;
};

/** \internal A convenience utility for determining if the type is a scalar.
 * This is used to enable some generic packet implementations.
 */
template<typename Packet>
struct is_scalar
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	enum
	{
		value = internal::is_same<Packet, Scalar>::value
	};
};

/** \internal \returns static_cast<TgtType>(a) (coeff-wise) */
template<typename SrcPacket, typename TgtPacket>
EIGEN_DEVICE_FUNC inline TgtPacket
pcast(const SrcPacket& a)
{
	return static_cast<TgtPacket>(a);
}
template<typename SrcPacket, typename TgtPacket>
EIGEN_DEVICE_FUNC inline TgtPacket
pcast(const SrcPacket& a, const SrcPacket& /*b*/)
{
	return static_cast<TgtPacket>(a);
}
template<typename SrcPacket, typename TgtPacket>
EIGEN_DEVICE_FUNC inline TgtPacket
pcast(const SrcPacket& a, const SrcPacket& /*b*/, const SrcPacket& /*c*/, const SrcPacket& /*d*/)
{
	return static_cast<TgtPacket>(a);
}
template<typename SrcPacket, typename TgtPacket>
EIGEN_DEVICE_FUNC inline TgtPacket
pcast(const SrcPacket& a,
	  const SrcPacket& /*b*/,
	  const SrcPacket& /*c*/,
	  const SrcPacket& /*d*/,
	  const SrcPacket& /*e*/,
	  const SrcPacket& /*f*/,
	  const SrcPacket& /*g*/,
	  const SrcPacket& /*h*/)
{
	return static_cast<TgtPacket>(a);
}

/** \internal \returns reinterpret_cast<Target>(a) */
template<typename Target, typename Packet>
EIGEN_DEVICE_FUNC inline Target
preinterpret(const Packet& a); /* { return reinterpret_cast<const Target&>(a); } */

/** \internal \returns a + b (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
padd(const Packet& a, const Packet& b)
{
	return a + b;
}
// Avoid compiler warning for boolean algebra.
template<>
EIGEN_DEVICE_FUNC inline bool
padd(const bool& a, const bool& b)
{
	return a || b;
}

/** \internal \returns a - b (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
psub(const Packet& a, const Packet& b)
{
	return a - b;
}

/** \internal \returns -a (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pnegate(const Packet& a)
{
	return -a;
}

template<>
EIGEN_DEVICE_FUNC inline bool
pnegate(const bool& a)
{
	return !a;
}

/** \internal \returns conj(a) (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pconj(const Packet& a)
{
	return numext::conj(a);
}

/** \internal \returns a * b (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pmul(const Packet& a, const Packet& b)
{
	return a * b;
}
// Avoid compiler warning for boolean algebra.
template<>
EIGEN_DEVICE_FUNC inline bool
pmul(const bool& a, const bool& b)
{
	return a && b;
}

/** \internal \returns a / b (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pdiv(const Packet& a, const Packet& b)
{
	return a / b;
}

// In the generic case, memset to all one bits.
template<typename Packet, typename EnableIf = void>
struct ptrue_impl
{
	static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/)
	{
		Packet b;
		memset(static_cast<void*>(&b), 0xff, sizeof(Packet));
		return b;
	}
};

// For non-trivial scalars, set to Scalar(1) (i.e. a non-zero value).
// Although this is technically not a valid bitmask, the scalar path for pselect
// uses a comparison to zero, so this should still work in most cases. We don't
// have another option, since the scalar type requires initialization.
template<typename T>
struct ptrue_impl<T, typename internal::enable_if<is_scalar<T>::value && NumTraits<T>::RequireInitialization>::type>
{
	static EIGEN_DEVICE_FUNC inline T run(const T& /*a*/) { return T(1); }
};

/** \internal \returns one bits. */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
ptrue(const Packet& a)
{
	return ptrue_impl<Packet>::run(a);
}

// In the general case, memset to zero.
template<typename Packet, typename EnableIf = void>
struct pzero_impl
{
	static EIGEN_DEVICE_FUNC inline Packet run(const Packet& /*a*/)
	{
		Packet b;
		memset(static_cast<void*>(&b), 0x00, sizeof(Packet));
		return b;
	}
};

// For scalars, explicitly set to Scalar(0), since the underlying representation
// for zero may not consist of all-zero bits.
template<typename T>
struct pzero_impl<T, typename internal::enable_if<is_scalar<T>::value>::type>
{
	static EIGEN_DEVICE_FUNC inline T run(const T& /*a*/) { return T(0); }
};

/** \internal \returns packet of zeros */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pzero(const Packet& a)
{
	return pzero_impl<Packet>::run(a);
}

/** \internal \returns a <= b as a bit mask */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pcmp_le(const Packet& a, const Packet& b)
{
	return a <= b ? ptrue(a) : pzero(a);
}

/** \internal \returns a < b as a bit mask */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pcmp_lt(const Packet& a, const Packet& b)
{
	return a < b ? ptrue(a) : pzero(a);
}

/** \internal \returns a == b as a bit mask */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pcmp_eq(const Packet& a, const Packet& b)
{
	return a == b ? ptrue(a) : pzero(a);
}

/** \internal \returns a < b or a==NaN or b==NaN as a bit mask */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pcmp_lt_or_nan(const Packet& a, const Packet& b)
{
	return a >= b ? pzero(a) : ptrue(a);
}

template<typename T>
struct bit_and
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a & b; }
};

template<typename T>
struct bit_or
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a | b; }
};

template<typename T>
struct bit_xor
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a, const T& b) const { return a ^ b; }
};

template<typename T>
struct bit_not
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR EIGEN_ALWAYS_INLINE T operator()(const T& a) const { return ~a; }
};

// Use operators &, |, ^, ~.
template<typename T>
struct operator_bitwise_helper
{
	EIGEN_DEVICE_FUNC static inline T bitwise_and(const T& a, const T& b) { return bit_and<T>()(a, b); }
	EIGEN_DEVICE_FUNC static inline T bitwise_or(const T& a, const T& b) { return bit_or<T>()(a, b); }
	EIGEN_DEVICE_FUNC static inline T bitwise_xor(const T& a, const T& b) { return bit_xor<T>()(a, b); }
	EIGEN_DEVICE_FUNC static inline T bitwise_not(const T& a) { return bit_not<T>()(a); }
};

// Apply binary operations byte-by-byte
template<typename T>
struct bytewise_bitwise_helper
{
	EIGEN_DEVICE_FUNC static inline T bitwise_and(const T& a, const T& b)
	{
		return binary(a, b, bit_and<unsigned char>());
	}
	EIGEN_DEVICE_FUNC static inline T bitwise_or(const T& a, const T& b)
	{
		return binary(a, b, bit_or<unsigned char>());
	}
	EIGEN_DEVICE_FUNC static inline T bitwise_xor(const T& a, const T& b)
	{
		return binary(a, b, bit_xor<unsigned char>());
	}
	EIGEN_DEVICE_FUNC static inline T bitwise_not(const T& a) { return unary(a, bit_not<unsigned char>()); }

  private:
	template<typename Op>
	EIGEN_DEVICE_FUNC static inline T unary(const T& a, Op op)
	{
		const unsigned char* a_ptr = reinterpret_cast<const unsigned char*>(&a);
		T c;
		unsigned char* c_ptr = reinterpret_cast<unsigned char*>(&c);
		for (size_t i = 0; i < sizeof(T); ++i) {
			*c_ptr++ = op(*a_ptr++);
		}
		return c;
	}

	template<typename Op>
	EIGEN_DEVICE_FUNC static inline T binary(const T& a, const T& b, Op op)
	{
		const unsigned char* a_ptr = reinterpret_cast<const unsigned char*>(&a);
		const unsigned char* b_ptr = reinterpret_cast<const unsigned char*>(&b);
		T c;
		unsigned char* c_ptr = reinterpret_cast<unsigned char*>(&c);
		for (size_t i = 0; i < sizeof(T); ++i) {
			*c_ptr++ = op(*a_ptr++, *b_ptr++);
		}
		return c;
	}
};

// In the general case, use byte-by-byte manipulation.
template<typename T, typename EnableIf = void>
struct bitwise_helper : public bytewise_bitwise_helper<T>
{};

// For integers or non-trivial scalars, use binary operators.
template<typename T>
struct bitwise_helper<T,
					  typename internal::enable_if<is_scalar<T>::value && (NumTraits<T>::IsInteger ||
																		   NumTraits<T>::RequireInitialization)>::type>
	: public operator_bitwise_helper<T>
{};

/** \internal \returns the bitwise and of \a a and \a b */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pand(const Packet& a, const Packet& b)
{
	return bitwise_helper<Packet>::bitwise_and(a, b);
}

/** \internal \returns the bitwise or of \a a and \a b */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
por(const Packet& a, const Packet& b)
{
	return bitwise_helper<Packet>::bitwise_or(a, b);
}

/** \internal \returns the bitwise xor of \a a and \a b */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pxor(const Packet& a, const Packet& b)
{
	return bitwise_helper<Packet>::bitwise_xor(a, b);
}

/** \internal \returns the bitwise not of \a a */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pnot(const Packet& a)
{
	return bitwise_helper<Packet>::bitwise_not(a);
}

/** \internal \returns the bitwise and of \a a and not \a b */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pandnot(const Packet& a, const Packet& b)
{
	return pand(a, pnot(b));
}

// In the general case, use bitwise select.
template<typename Packet, typename EnableIf = void>
struct pselect_impl
{
	static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b)
	{
		return por(pand(a, mask), pandnot(b, mask));
	}
};

// For scalars, use ternary select.
template<typename Packet>
struct pselect_impl<Packet, typename internal::enable_if<is_scalar<Packet>::value>::type>
{
	static EIGEN_DEVICE_FUNC inline Packet run(const Packet& mask, const Packet& a, const Packet& b)
	{
		return numext::equal_strict(mask, Packet(0)) ? b : a;
	}
};

/** \internal \returns \a or \b for each field in packet according to \mask */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pselect(const Packet& mask, const Packet& a, const Packet& b)
{
	return pselect_impl<Packet>::run(mask, a, b);
}

template<>
EIGEN_DEVICE_FUNC inline bool
pselect<bool>(const bool& cond, const bool& a, const bool& b)
{
	return cond ? a : b;
}

/** \internal \returns the min or of \a a and \a b (coeff-wise)
	If either \a a or \a b are NaN, the result is implementation defined. */
template<int NaNPropagation>
struct pminmax_impl
{
	template<typename Packet, typename Op>
	static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op)
	{
		return op(a, b);
	}
};

/** \internal \returns the min or max of \a a and \a b (coeff-wise)
	If either \a a or \a b are NaN, NaN is returned. */
template<>
struct pminmax_impl<PropagateNaN>
{
	template<typename Packet, typename Op>
	static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op)
	{
		Packet not_nan_mask_a = pcmp_eq(a, a);
		Packet not_nan_mask_b = pcmp_eq(b, b);
		return pselect(not_nan_mask_a, pselect(not_nan_mask_b, op(a, b), b), a);
	}
};

/** \internal \returns the min or max of \a a and \a b (coeff-wise)
	If both \a a and \a b are NaN, NaN is returned.
	Equivalent to std::fmin(a, b).  */
template<>
struct pminmax_impl<PropagateNumbers>
{
	template<typename Packet, typename Op>
	static EIGEN_DEVICE_FUNC inline Packet run(const Packet& a, const Packet& b, Op op)
	{
		Packet not_nan_mask_a = pcmp_eq(a, a);
		Packet not_nan_mask_b = pcmp_eq(b, b);
		return pselect(not_nan_mask_a, pselect(not_nan_mask_b, op(a, b), a), b);
	}
};

#ifndef SYCL_DEVICE_ONLY
#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) Func
#else
#define EIGEN_BINARY_OP_NAN_PROPAGATION(Type, Func) [](const Type& a, const Type& b) { return Func(a, b); }
#endif

/** \internal \returns the min of \a a and \a b  (coeff-wise).
	If \a a or \b b is NaN, the return value is implementation defined. */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pmin(const Packet& a, const Packet& b)
{
	return numext::mini(a, b);
}

/** \internal \returns the min of \a a and \a b  (coeff-wise).
	NaNPropagation determines the NaN propagation semantics. */
template<int NaNPropagation, typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pmin(const Packet& a, const Packet& b)
{
	return pminmax_impl<NaNPropagation>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmin<Packet>)));
}

/** \internal \returns the max of \a a and \a b  (coeff-wise)
	If \a a or \b b is NaN, the return value is implementation defined. */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pmax(const Packet& a, const Packet& b)
{
	return numext::maxi(a, b);
}

/** \internal \returns the max of \a a and \a b  (coeff-wise).
	NaNPropagation determines the NaN propagation semantics. */
template<int NaNPropagation, typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pmax(const Packet& a, const Packet& b)
{
	return pminmax_impl<NaNPropagation>::run(a, b, EIGEN_BINARY_OP_NAN_PROPAGATION(Packet, (pmax<Packet>)));
}

/** \internal \returns the absolute value of \a a */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pabs(const Packet& a)
{
	return numext::abs(a);
}
template<>
EIGEN_DEVICE_FUNC inline unsigned int
pabs(const unsigned int& a)
{
	return a;
}
template<>
EIGEN_DEVICE_FUNC inline unsigned long
pabs(const unsigned long& a)
{
	return a;
}
template<>
EIGEN_DEVICE_FUNC inline unsigned long long
pabs(const unsigned long long& a)
{
	return a;
}

/** \internal \returns the addsub value of \a a,b */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
paddsub(const Packet& a, const Packet& b)
{
	return pselect(peven_mask(a), padd(a, b), psub(a, b));
}

/** \internal \returns the phase angle of \a a */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
parg(const Packet& a)
{
	using numext::arg;
	return arg(a);
}

/** \internal \returns \a a logically shifted by N bits to the right */
template<int N>
EIGEN_DEVICE_FUNC inline int
parithmetic_shift_right(const int& a)
{
	return a >> N;
}
template<int N>
EIGEN_DEVICE_FUNC inline long int
parithmetic_shift_right(const long int& a)
{
	return a >> N;
}

/** \internal \returns \a a arithmetically shifted by N bits to the right */
template<int N>
EIGEN_DEVICE_FUNC inline int
plogical_shift_right(const int& a)
{
	return static_cast<int>(static_cast<unsigned int>(a) >> N);
}
template<int N>
EIGEN_DEVICE_FUNC inline long int
plogical_shift_right(const long int& a)
{
	return static_cast<long>(static_cast<unsigned long>(a) >> N);
}

/** \internal \returns \a a shifted by N bits to the left */
template<int N>
EIGEN_DEVICE_FUNC inline int
plogical_shift_left(const int& a)
{
	return a << N;
}
template<int N>
EIGEN_DEVICE_FUNC inline long int
plogical_shift_left(const long int& a)
{
	return a << N;
}

/** \internal \returns the significant and exponent of the underlying floating point numbers
 * See https://en.cppreference.com/w/cpp/numeric/math/frexp
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pfrexp(const Packet& a, Packet& exponent)
{
	int exp;
	EIGEN_USING_STD(frexp);
	Packet result = static_cast<Packet>(frexp(a, &exp));
	exponent = static_cast<Packet>(exp);
	return result;
}

/** \internal \returns a * 2^((int)exponent)
 * See https://en.cppreference.com/w/cpp/numeric/math/ldexp
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pldexp(const Packet& a, const Packet& exponent)
{
	EIGEN_USING_STD(ldexp)
	return static_cast<Packet>(ldexp(a, static_cast<int>(exponent)));
}

/** \internal \returns the min of \a a and \a b  (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pabsdiff(const Packet& a, const Packet& b)
{
	return pselect(pcmp_lt(a, b), psub(b, a), psub(a, b));
}

/** \internal \returns a packet version of \a *from, from must be 16 bytes aligned */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pload(const typename unpacket_traits<Packet>::type* from)
{
	return *from;
}

/** \internal \returns a packet version of \a *from, (un-aligned load) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
ploadu(const typename unpacket_traits<Packet>::type* from)
{
	return *from;
}

/** \internal \returns a packet version of \a *from, (un-aligned masked load)
 * There is no generic implementation. We only have implementations for specialized
 * cases. Generic case should not be called.
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline typename enable_if<unpacket_traits<Packet>::masked_load_available, Packet>::type
ploadu(const typename unpacket_traits<Packet>::type* from, typename unpacket_traits<Packet>::mask_t umask);

/** \internal \returns a packet with constant coefficients \a a, e.g.: (a,a,a,a) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pset1(const typename unpacket_traits<Packet>::type& a)
{
	return a;
}

/** \internal \returns a packet with constant coefficients set from bits */
template<typename Packet, typename BitsType>
EIGEN_DEVICE_FUNC inline Packet
pset1frombits(BitsType a);

/** \internal \returns a packet with constant coefficients \a a[0], e.g.: (a[0],a[0],a[0],a[0]) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pload1(const typename unpacket_traits<Packet>::type* a)
{
	return pset1<Packet>(*a);
}

/** \internal \returns a packet with elements of \a *from duplicated.
 * For instance, for a packet of 8 elements, 4 scalars will be read from \a *from and
 * duplicated to form: {from[0],from[0],from[1],from[1],from[2],from[2],from[3],from[3]}
 * Currently, this function is only used for scalar * complex products.
 */
template<typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
ploaddup(const typename unpacket_traits<Packet>::type* from)
{
	return *from;
}

/** \internal \returns a packet with elements of \a *from quadrupled.
 * For instance, for a packet of 8 elements, 2 scalars will be read from \a *from and
 * replicated to form: {from[0],from[0],from[0],from[0],from[1],from[1],from[1],from[1]}
 * Currently, this function is only used in matrix products.
 * For packet-size smaller or equal to 4, this function is equivalent to pload1
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
ploadquad(const typename unpacket_traits<Packet>::type* from)
{
	return pload1<Packet>(from);
}

/** \internal equivalent to
 * \code
 * a0 = pload1(a+0);
 * a1 = pload1(a+1);
 * a2 = pload1(a+2);
 * a3 = pload1(a+3);
 * \endcode
 * \sa pset1, pload1, ploaddup, pbroadcast2
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline void
pbroadcast4(const typename unpacket_traits<Packet>::type* a, Packet& a0, Packet& a1, Packet& a2, Packet& a3)
{
	a0 = pload1<Packet>(a + 0);
	a1 = pload1<Packet>(a + 1);
	a2 = pload1<Packet>(a + 2);
	a3 = pload1<Packet>(a + 3);
}

/** \internal equivalent to
 * \code
 * a0 = pload1(a+0);
 * a1 = pload1(a+1);
 * \endcode
 * \sa pset1, pload1, ploaddup, pbroadcast4
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline void
pbroadcast2(const typename unpacket_traits<Packet>::type* a, Packet& a0, Packet& a1)
{
	a0 = pload1<Packet>(a + 0);
	a1 = pload1<Packet>(a + 1);
}

/** \internal \brief Returns a packet with coefficients (a,a+1,...,a+packet_size-1). */
template<typename Packet>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Packet
plset(const typename unpacket_traits<Packet>::type& a)
{
	return a;
}

/** \internal \returns a packet with constant coefficients \a a, e.g.: (x, 0, x, 0),
	 where x is the value of all 1-bits. */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
peven_mask(const Packet& /*a*/)
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	const size_t n = unpacket_traits<Packet>::size;
	EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n];
	for (size_t i = 0; i < n; ++i) {
		memset(elements + i, ((i & 1) == 0 ? 0xff : 0), sizeof(Scalar));
	}
	return ploadu<Packet>(elements);
}

/** \internal copy the packet \a from to \a *to, \a to must be 16 bytes aligned */
template<typename Scalar, typename Packet>
EIGEN_DEVICE_FUNC inline void
pstore(Scalar* to, const Packet& from)
{
	(*to) = from;
}

/** \internal copy the packet \a from to \a *to, (un-aligned store) */
template<typename Scalar, typename Packet>
EIGEN_DEVICE_FUNC inline void
pstoreu(Scalar* to, const Packet& from)
{
	(*to) = from;
}

/** \internal copy the packet \a from to \a *to, (un-aligned store with a mask)
 * There is no generic implementation. We only have implementations for specialized
 * cases. Generic case should not be called.
 */
template<typename Scalar, typename Packet>
EIGEN_DEVICE_FUNC inline typename enable_if<unpacket_traits<Packet>::masked_store_available, void>::type
pstoreu(Scalar* to, const Packet& from, typename unpacket_traits<Packet>::mask_t umask);

template<typename Scalar, typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pgather(const Scalar* from, Index /*stride*/)
{
	return ploadu<Packet>(from);
}

template<typename Scalar, typename Packet>
EIGEN_DEVICE_FUNC inline void
pscatter(Scalar* to, const Packet& from, Index /*stride*/)
{
	pstore(to, from);
}

/** \internal tries to do cache prefetching of \a addr */
template<typename Scalar>
EIGEN_DEVICE_FUNC inline void
prefetch(const Scalar* addr)
{
#if defined(EIGEN_HIP_DEVICE_COMPILE)
	// do nothing
#elif defined(EIGEN_CUDA_ARCH)
#if defined(__LP64__) || EIGEN_OS_WIN64
	// 64-bit pointer operand constraint for inlined asm
	asm(" prefetch.L1 [ %1 ];" : "=l"(addr) : "l"(addr));
#else
	// 32-bit pointer operand constraint for inlined asm
	asm(" prefetch.L1 [ %1 ];" : "=r"(addr) : "r"(addr));
#endif
#elif (!EIGEN_COMP_MSVC) && (EIGEN_COMP_GNUC || EIGEN_COMP_CLANG || EIGEN_COMP_ICC)
	__builtin_prefetch(addr);
#endif
}

/** \internal \returns the reversed elements of \a a*/
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
preverse(const Packet& a)
{
	return a;
}

/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pcplxflip(const Packet& a)
{
	return Packet(numext::imag(a), numext::real(a));
}

/**************************
 * Special math functions
 ***************************/

/** \internal \returns the sine of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
psin(const Packet& a)
{
	EIGEN_USING_STD(sin);
	return sin(a);
}

/** \internal \returns the cosine of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pcos(const Packet& a)
{
	EIGEN_USING_STD(cos);
	return cos(a);
}

/** \internal \returns the tan of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
ptan(const Packet& a)
{
	EIGEN_USING_STD(tan);
	return tan(a);
}

/** \internal \returns the arc sine of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pasin(const Packet& a)
{
	EIGEN_USING_STD(asin);
	return asin(a);
}

/** \internal \returns the arc cosine of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pacos(const Packet& a)
{
	EIGEN_USING_STD(acos);
	return acos(a);
}

/** \internal \returns the arc tangent of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
patan(const Packet& a)
{
	EIGEN_USING_STD(atan);
	return atan(a);
}

/** \internal \returns the hyperbolic sine of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
psinh(const Packet& a)
{
	EIGEN_USING_STD(sinh);
	return sinh(a);
}

/** \internal \returns the hyperbolic cosine of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pcosh(const Packet& a)
{
	EIGEN_USING_STD(cosh);
	return cosh(a);
}

/** \internal \returns the hyperbolic tan of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
ptanh(const Packet& a)
{
	EIGEN_USING_STD(tanh);
	return tanh(a);
}

/** \internal \returns the exp of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pexp(const Packet& a)
{
	EIGEN_USING_STD(exp);
	return exp(a);
}

/** \internal \returns the expm1 of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pexpm1(const Packet& a)
{
	return numext::expm1(a);
}

/** \internal \returns the log of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
plog(const Packet& a)
{
	EIGEN_USING_STD(log);
	return log(a);
}

/** \internal \returns the log1p of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
plog1p(const Packet& a)
{
	return numext::log1p(a);
}

/** \internal \returns the log10 of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
plog10(const Packet& a)
{
	EIGEN_USING_STD(log10);
	return log10(a);
}

/** \internal \returns the log10 of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
plog2(const Packet& a)
{
	typedef typename internal::unpacket_traits<Packet>::type Scalar;
	return pmul(pset1<Packet>(Scalar(EIGEN_LOG2E)), plog(a));
}

/** \internal \returns the square-root of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
psqrt(const Packet& a)
{
	return numext::sqrt(a);
}

/** \internal \returns the reciprocal square-root of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
prsqrt(const Packet& a)
{
	typedef typename internal::unpacket_traits<Packet>::type Scalar;
	return pdiv(pset1<Packet>(Scalar(1)), psqrt(a));
}

/** \internal \returns the rounded value of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pround(const Packet& a)
{
	using numext::round;
	return round(a);
}

/** \internal \returns the floor of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pfloor(const Packet& a)
{
	using numext::floor;
	return floor(a);
}

/** \internal \returns the rounded value of \a a (coeff-wise) with current
 * rounding mode */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
print(const Packet& a)
{
	using numext::rint;
	return rint(a);
}

/** \internal \returns the ceil of \a a (coeff-wise) */
template<typename Packet>
EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS Packet
pceil(const Packet& a)
{
	using numext::ceil;
	return ceil(a);
}

/** \internal \returns the first element of a packet */
template<typename Packet>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
pfirst(const Packet& a)
{
	return a;
}

/** \internal \returns the sum of the elements of upper and lower half of \a a if \a a is larger than 4.
 * For a packet {a0, a1, a2, a3, a4, a5, a6, a7}, it returns a half packet {a0+a4, a1+a5, a2+a6, a3+a7}
 * For packet-size smaller or equal to 4, this boils down to a noop.
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline
	typename conditional<(unpacket_traits<Packet>::size % 8) == 0, typename unpacket_traits<Packet>::half, Packet>::type
	predux_half_dowto4(const Packet& a)
{
	return a;
}

// Slow generic implementation of Packet reduction.
template<typename Packet, typename Op>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
predux_helper(const Packet& a, Op op)
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	const size_t n = unpacket_traits<Packet>::size;
	EIGEN_ALIGN_TO_BOUNDARY(sizeof(Packet)) Scalar elements[n];
	pstoreu<Scalar>(elements, a);
	for (size_t k = n / 2; k > 0; k /= 2) {
		for (size_t i = 0; i < k; ++i) {
			elements[i] = op(elements[i], elements[i + k]);
		}
	}
	return elements[0];
}

/** \internal \returns the sum of the elements of \a a*/
template<typename Packet>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
predux(const Packet& a)
{
	return a;
}

/** \internal \returns the product of the elements of \a a */
template<typename Packet>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
predux_mul(const Packet& a)
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmul<Scalar>)));
}

/** \internal \returns the min of the elements of \a a */
template<typename Packet>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
predux_min(const Packet& a)
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<PropagateFast, Scalar>)));
}

template<int NaNPropagation, typename Packet>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
predux_min(const Packet& a)
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmin<NaNPropagation, Scalar>)));
}

/** \internal \returns the min of the elements of \a a */
template<typename Packet>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
predux_max(const Packet& a)
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<PropagateFast, Scalar>)));
}

template<int NaNPropagation, typename Packet>
EIGEN_DEVICE_FUNC inline typename unpacket_traits<Packet>::type
predux_max(const Packet& a)
{
	typedef typename unpacket_traits<Packet>::type Scalar;
	return predux_helper(a, EIGEN_BINARY_OP_NAN_PROPAGATION(Scalar, (pmax<NaNPropagation, Scalar>)));
}

#undef EIGEN_BINARY_OP_NAN_PROPAGATION

/** \internal \returns true if all coeffs of \a a means "true"
 * It is supposed to be called on values returned by pcmp_*.
 */
// not needed yet
// template<typename Packet> EIGEN_DEVICE_FUNC inline bool predux_all(const Packet& a)
// { return bool(a); }

/** \internal \returns true if any coeffs of \a a means "true"
 * It is supposed to be called on values returned by pcmp_*.
 */
template<typename Packet>
EIGEN_DEVICE_FUNC inline bool
predux_any(const Packet& a)
{
	// Dirty but generic implementation where "true" is assumed to be non 0 and all the sames.
	// It is expected that "true" is either:
	//  - Scalar(1)
	//  - bits full of ones (NaN for floats),
	//  - or first bit equals to 1 (1 for ints, smallest denormal for floats).
	// For all these cases, taking the sum is just fine, and this boils down to a no-op for scalars.
	typedef typename unpacket_traits<Packet>::type Scalar;
	return numext::not_equal_strict(predux(a), Scalar(0));
}

/***************************************************************************
 * The following functions might not have to be overwritten for vectorized types
 ***************************************************************************/

/** \internal copy a packet with constant coefficient \a a (e.g., [a,a,a,a]) to \a *to. \a to must be 16 bytes aligned
 */
// NOTE: this function must really be templated on the packet type (think about different packet types for the same
// scalar type)
template<typename Packet>
inline void
pstore1(typename unpacket_traits<Packet>::type* to, const typename unpacket_traits<Packet>::type& a)
{
	pstore(to, pset1<Packet>(a));
}

/** \internal \returns a * b + c (coeff-wise) */
template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pmadd(const Packet& a, const Packet& b, const Packet& c)
{
	return padd(pmul(a, b), c);
}

/** \internal \returns a packet version of \a *from.
 * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
template<typename Packet, int Alignment>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet
ploadt(const typename unpacket_traits<Packet>::type* from)
{
	if (Alignment >= unpacket_traits<Packet>::alignment)
		return pload<Packet>(from);
	else
		return ploadu<Packet>(from);
}

/** \internal copy the packet \a from to \a *to.
 * The pointer \a from must be aligned on a \a Alignment bytes boundary. */
template<typename Scalar, typename Packet, int Alignment>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE void
pstoret(Scalar* to, const Packet& from)
{
	if (Alignment >= unpacket_traits<Packet>::alignment)
		pstore(to, from);
	else
		pstoreu(to, from);
}

/** \internal \returns a packet version of \a *from.
 * Unlike ploadt, ploadt_ro takes advantage of the read-only memory path on the
 * hardware if available to speedup the loading of data that won't be modified
 * by the current computation.
 */
template<typename Packet, int LoadMode>
EIGEN_DEVICE_FUNC EIGEN_ALWAYS_INLINE Packet
ploadt_ro(const typename unpacket_traits<Packet>::type* from)
{
	return ploadt<Packet, LoadMode>(from);
}

/***************************************************************************
 * Fast complex products (GCC generates a function call which is very slow)
 ***************************************************************************/

// Eigen+CUDA does not support complexes.
#if !defined(EIGEN_GPUCC)

template<>
inline std::complex<float>
pmul(const std::complex<float>& a, const std::complex<float>& b)
{
	return std::complex<float>(a.real() * b.real() - a.imag() * b.imag(), a.imag() * b.real() + a.real() * b.imag());
}

template<>
inline std::complex<double>
pmul(const std::complex<double>& a, const std::complex<double>& b)
{
	return std::complex<double>(a.real() * b.real() - a.imag() * b.imag(), a.imag() * b.real() + a.real() * b.imag());
}

#endif

/***************************************************************************
 * PacketBlock, that is a collection of N packets where the number of words
 * in the packet is a multiple of N.
 ***************************************************************************/
template<typename Packet, int N = unpacket_traits<Packet>::size>
struct PacketBlock
{
	Packet packet[N];
};

template<typename Packet>
EIGEN_DEVICE_FUNC inline void
ptranspose(PacketBlock<Packet, 1>& /*kernel*/)
{
	// Nothing to do in the scalar case, i.e. a 1x1 matrix.
}

/***************************************************************************
 * Selector, i.e. vector of N boolean values used to select (i.e. blend)
 * words from 2 packets.
 ***************************************************************************/
template<size_t N>
struct Selector
{
	bool select[N];
};

template<typename Packet>
EIGEN_DEVICE_FUNC inline Packet
pblend(const Selector<unpacket_traits<Packet>::size>& ifPacket, const Packet& thenPacket, const Packet& elsePacket)
{
	return ifPacket.select[0] ? thenPacket : elsePacket;
}

} // end namespace internal

} // end namespace Eigen

#endif // EIGEN_GENERIC_PACKET_MATH_H
